Question: A circle has a sector with area $8\pi$ and central angle $80^\circ$. What is the area of the circle? ${36\pi}$ $\color{#9D38BD}{80^\circ}$ ${8\pi}$
Answer: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{80^\circ}{360^\circ} = 8\pi \div A_c$ $\dfrac{2}{9} = 8\pi \div A_c$ $A_c \times \dfrac{2}{9} = 8\pi$ $A_c = 8\pi \times \dfrac{9}{2}$ $A_c = 36\pi$